# Direction indices

### From Online Dictionary of Crystallography

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Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the '''direction indices'''. | Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the '''direction indices'''. | ||

- | In the three-dimensional space, the direction passing through the origin and the lattice nodes ''nu'',''nv'',''nw'', where ''n'' is an integer, has direction indices [''uvw'']. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-''u'', -''v'' | + | In the three-dimensional space, the direction passing through the origin and the lattice nodes ''nu'',''nv'',''nw'', where ''n'' is an integer, has direction indices [''uvw'']. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-''u'', -''v'', -''w''] identify the same direction as [''uvw''] simply observed from the opposite side. |

When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted. | When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted. |

## Revision as of 10:16, 1 September 2017

Indices de direction (*Fr*); Indices de dirección (*Sp*); Indici di direzione (*It*); 方向指数 (*Ja*).

Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the **direction indices**.

In the three-dimensional space, the direction passing through the origin and the lattice nodes *nu*,*nv*,*nw*, where *n* is an integer, has direction indices [*uvw*]. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-*u*, -*v*, -*w*] identify the same direction as [*uvw*] simply observed from the opposite side.

When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.